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# Ajima-Malfatti Points

The lines connecting the vertices and corresponding circle-circle intersections in Malfatti's problem coincide in a point called the first Ajima-Malfatti point (Kimberling and MacDonald 1990, Kimberling 1994). This point has triangle center function

Similarly, letting , , and be the excenters of , then the lines , , and are coincident in another point called the second Ajima-Malfatti point, which is Kimberling center (but is at present given erroneously in Kimberling's tabulation).

These points are sometimes simply called the Malfatti points (Kimberling 1994).

Malfatti Circles, Malfatti's Problem, Sangaku Problem, Tangent Circles

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## References

Fukagawa, H. and Pedoe, D. Japanese Temple Geometry Problems. Winnipeg, Manitoba, Canada: Charles Babbage Research Foundation, 1989.Goldberg, M. "On the Original Malfatti Problem." Math. Mag. 40, 241-247, 1967.Kimberling, C. "Central Points and Central Lines in the Plane of a Triangle." Math. Mag. 67, 163-187, 1994.Kimberling, C. "1st and 2nd Ajima-Malfatti Points." http://faculty.evansville.edu/ck6/tcenters/recent/ajmalf.html.Kimberling, C. "Encyclopedia of Triangle Centers: X(179)=1st Ajima-Malfatti Point." http://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X179.Kimberling, C. "Encyclopedia of Triangle Centers: X(180)=2nd Ajima-Malfatti Point." http://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X180.Kimberling, C. and MacDonald, I. G. "Problem E 3251 and Solution." Amer. Math. Monthly 97, 612-613, 1990.

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Ajima-Malfatti Points

## Cite this as:

Weisstein, Eric W. "Ajima-Malfatti Points." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Ajima-MalfattiPoints.html